Cooperativity and Entanglement of Atom-field States

Abstract

The Jaynes-Cummings model of a single two-level atom interacting with a quantized single-mode coherent field generates at the half-revival time a dynamically disentangled atom-field state. At such times, the field is in asymptotically pure Schrödinger cat state, a macroscopic superposition of distinct field eigenmodes. In this paper we address the problem of field purity when a second atom is allowed to interact with the cavity mode and becomes entangled with the first atom via their mutual cavity field with which they interact. We employ the collective Dicke states to describe the cooperative effects on the entanglement and show that the second atom spoils the purity of the field state except for special cases of the atom-field coupling or of initial conditions.     

Interaction of Squeezed Light with Two-level Atoms

Abstract

We investigate some of the fundamental features of the interaction of squeezed light with two-level atoms in the framework of the Jaynes-Cummings model. We start our analysis by calculating the collapses and revivals of the atomic inversion. We discuss the degree of purity of the field (given by the entropy) and its disentanglement from the atomic source. The connection with the evolution of the Q-function is also made. We notice that contrary to the coherent state case, the field turns into a nearly pure (squeezed) state at the revival time as if the field was prepared in a coherent state. The field also becomes a superposition of squeezed states at half of the revival time, and this is confirmed by investigating the photon number distribution. The phase properties of the field are discussed using the Pegg-Barnett formalism.     

Non-conditioned generation of Schrödinger cat states in a cavity

We investigate the dynamics of a two-level atom in a cavity filled with a nonlinear medium. We show that the atom-field detuning δ and the nonlinear parameter χ⁽³⁾ may be combined to yield a periodic dynamics, allowing the generation of almost exact superpositions of coherent states (Schrödinger cats). By analysing the atomic inversion and the field purity, we verify that any initial atom-field state is recovered at each revival time, and that a coherent field interacting with an excited atom evolves to a superposition of coherent states at each collapse time. We show that a mixed field state (statistical mixture of two coherent states) evolves towards an almost pure field state as well (Schrödinger cat). We discuss the validity of these results by using the field fidelity and the Wigner function.     

Interaction of Superpositions of Coherent States of Light with Two-level Atoms

Abstract

We investigate some of the basic features of the interaction of superpositions of coherent states of light with two-level atoms in the framework of the Jaynes-Cummings model. We compare the behaviour of the system in the case of having a coherent superposition state and a statistical mixture of coherent states as an initial field. We investigate the collapses and revivals of the atomic inversion by studying the evolution of the Q function of the cavity field. We also establish the connection between the purity of the field and the collapses and revivals of the atomic inversion.     

On the Interaction of Two-level Atoms with Superpositions of Coherent States of Light

Abstract

In this paper we study the decoherence process occurring when a field prepared in quantum superpositions of coherent states (Schrödinger cats) interacts with a two-level atom in the framework of the Jaynes-Cummings model. We emphasize the influence of the relative phase in the initial superposition state on the purity of the field during the evolution     

Study of Photon Antibunching in the Vacuum Field Two-photon Jaynes-Cummings Model Without the Rotating-wave Approximation

Abstract

We have numerically investigated photon antibunching in the two-photon Jaynes-Cummings model without the rotating-wave approximation when the system is restricted to the following initial condition: the atom in the excited state and the field in the vacuum state. The influence of the detuning Δ on photon antibunching has also been discussed.     

Nonlinear Dissipative Oscillator with Displaced Number States

Abstract

We study the interaction of a Kerr-like medium with light initially prepared in a displaced number state. We analyse squeezing properties and photon statistics at the output of a Kerr-like medium. We show that under certain conditions the superposition of two displaced number states can be created. We study the influence of dissipation on the formation of the superposition state.     

N-level Atom Interacting with Single-mode Radiation Field: An Exactly Solvable Model with Multiphoton Transitions and Intensity-dependent Coupling

Abstract

We study the dynamics of an N-level atom coupled in a lossless cavity to a single-mode near-resonant quantized field. The atomic levels are coupled by the multiphoton transitions and the coupling constants between the field and the atomic levels are supposed to be intensity dependent. We find the exact solution for the state vector describing the dynamics of the atom-plus-field system. As an illustration we use the model for studying (i) the time evolution of the atomic occupation probability with the initially coherent field and (ii) the light squeezing, when the cavity field is initially in the vacuum state and the atom is prepared in the atomic ‘coherent state’ (a superposition of atomic states).     

Thermal Equilibrium in the Jaynes-Cummings Model

Abstract

The master equation currently used to describe a two level atom interacting with a single mode field damped by contact with a thermal reservoir (the damped Jaynes-Cummings model) is shown not to have, as its steady state solution, the expected canonical density operator prescribed by the general principles of statistical mechanics for a system in thermal equilibrium. A modified master equation is derived here which satisfies this requirement. Except for a reservoir at zero temperature, this master equation differs from that which is currently used in that the damping terms contain contributions due to the atom-field interaction.     

Emission Spectra of a Two-level Atom Under the Presence of Another Two-level Atom

Abstract

We investigate the spectrum of light emitted by a two-level atom interacting with another two-level atom inside an ideal cavity within the frame of generalized Jaynes-Cummings model. The influence of various ratios of the coupling constants of the atoms to the field on the spectrum of the emitted light is studied in detail for the case when the atoms are supposed to be initially in the excited state and the field in a Fock state as well as their superposition.     

Cavity field spectrum for multiphoton Jaynes-Cummings model

Abstract

The field spectra in an ideal cavity for the multiphoton Jaynes-Cummings model are studied. The analytical expression for the spectrum is obtained from the finite double-Fourier transform of the two-time field correlation function. The spectral differences between the initial coherent and initial thermal states are discussed, and the comparisons between the field spectra and atomic emission spectra for k = 2, 3 and 4 are presented. It is shown that the kth power of the photon annihilation operator and atomic lowering operator are subjected to identical forms of a second-order differential equation, in which the coefficients consist of the constants of motion. The field spectrum in the cavity and the emission spectrum of the atom for the initial vacuum state are compared.     

Population trapping in the Jaynes-Cummings model with a Kerr nonlinearity in the cavity

Abstract

An electromagnetic field state is found which maintains the population inversion of the atom stationary during the interaction with the field through a Jaynes-Cummings model (JCM) with a Kerr type nonlinearity in the cavity. The condition of stationarity of the population inversion includes the phase coupling of atomic dipole with the field. We have shown that the Kerr nonlinearity in the cavity field significantly modifies the photon statistics of the trapped field state through an intensity dependent detuning in the field compared to the normal JCM trapping state. We have also demonstrated the novel features of sub-Poissonian character and the squeezing of the trapped field state. The dynamics of the initial trapped field is studied in terms of squeezing and the Q-function.     

Determining the state of a single cavity mode from photon statistics

Abstract

We present various schemes for measuring the quantum state of a single mode of the electromagnetic field. These involve measuring the photon statistics for the mode before and after an interaction with either one or two two-level atoms. The photon statistics conditioned on the final state of the atoms, for two choices of the initial set of atomic states, along with the initial photon statistics, may be used to calculate the complete quantum state in a simple manner. Alternatively, when one atom is used, two unconditioned sets of photon statistics, each after interaction with a single atom in different initial states, along with the initial photon statistics may be used to calculate the initial state in a simple manner. When the cavity is allowed to interact with just one atom, only pure cavity states which do not contain zeros in the photon distribution may be reconstructed. When two atoms are used we may reconstruct pure states which do not contain adjacent zeros in the photon distribution. Coherent states and number states are among those that may be measured with one-atom interaction, and squeezed states and ?Schrödinger cats‘ are among those that may be measured with a two-atom interaction.     

Quantum states engineering: Recurrence formula including states with even and odd numbers of photons

Abstract

A previous recurrence formula using the resonant atom-field interaction for the generation of a field state in a cavity is extended to arbitrary states having even and odd numbers of photons in their photon-number distribution.     

Production of Macroscopic Schrödinger Cat States from Weak Quantized Cavity Fields Interacting with Atoms Driven by Classical Fields

Abstract

We show that macroscopic superposition (Schrödinger cat) states of a quantized single-mode cavity field can be produced via the interaction of this field with a two-level atom which is driven by a classical field even for small initial intensities of the quantized cavity mode. We show that with a properly chosen driving field an almost pure superposition state with arbitrary amplitudes and phases of component states can be produced.     

Kerr cat states from the four-photon Jaynes-Cummings model

We investigate the dynamics of a four-photon Jaynes—Cummings model for large photon number. It is shown that at certain times the cavity field is in a pure state which is a superposition of two Kerr states, analogous to the Schrödinger cat state (superposition of two coherent states) which occurs in the one and two photon cases.     

Controlling decoherence of a two-level atom in a lossy cavity

Abstract

By use of external periodic driving sources, we demonstrate the possibility of controlling the coherent as well as the decoherent dynamics of a two-level atom placed in a lossy cavity. The control of the coherent dynamics is elucidated for the phenomenon of coherent destruction of tunnelling (CDT), i.e. the coherent dynamics of a driven two-level atom in a quantum superposition state can be brought practically to a complete standstill. We study this phenomenon for different initial preparations of the two-level atom. We then proceed to investigate the decoherence originating from the interaction of the two-level atom with a lossy cavity mode. The loss mechanism is described in terms of a microscopic model that couples the cavity mode to a bath of harmonic field modes. A suitably tuned external cw-laser field applied to the two-level atom slows down considerably the decoherence of the atom. We demonstrate the suppression of decoherence for two opposite initial preparations of the atomic state: a quantum superposition state as well as the ground state. These findings can be used to decrease the influence of decoherence in qubit manipulation processes.     

Atomic Dipole Dynamics in the Thermal Quantized Cavity Field

Abstract

We consider the resonant interaction of a two-level atom with a thermal state of the quantized field in a lossless cavity. Non-trivial dynamics of the atomic dipole moment and the field quadrature components arise if the atom is initially prepared in a coherent superposition of its upper and lower states. In particular, the initial thermal field state acquires a well defined phase that corresponds to the initial phase of the superposition atomic state. Population trapping occurs when the intensity grows.     

Quantum dynamical properties of a two-photon non linear Jaynes-cummings model

Abstract

In this paper a two-photon Jaynes-Cummings model interacting with a Kerr-like medium is studied. It is assumed that the electromagnetic field is in different states such as coherent, squeezed vacuum and pair coherent, and that the atom is initially in the excited state. The temporal evolution of the population of the excited level, and the second-order coherence function are studied. The results obtained show that this system has some similarities with the two-mode Stark system. Two photon entanglement are analysed at different initial conditions.     

Collapse-revival Phenomenon in the Process of k-photon Down Conversion with Superpositions of Number States

Abstract

We calculate numerically the time evolution of the mean photon number in the process of k-photon down conversion process with quantized pump. The pump mode was supposed to be initially in a superposition of number states and the down converted mode in a number state. We analysed in some detail the influence of the initial field statistics of the pump mode as well as the presence of non-vacuum number states in the down converted mode on the appearance of collapses and revivals.